How to Import a transparent .SVG file to blender, and convert it to a 3D object?
I've made two things in Illustrator and it was imported correctly:


Select your shape and, in the Pathfinder window, click the Unite tool.
Scale it very big (like 1000%)


then save and, in Blender, Import > SVG.

To make it a mesh: Select the object and alt C > Mesh From Curve

You can simplify the mesh a lot in Edit mode with X > Limited Dissolve, and W > Remove Doubles

It will display black even if you apply a white material but you can change it in the Properties > Material > Settings > Viewport Colors